Find the total area enclosed between y = x^3 - x, the x axis and the lines x = 1 and x= -1 . (Why do i get 0 as an answer?)

Our first step should always be to make sure we understand what the question actually wants from us, in the case of most polynomial questions a rough sketch with any information we know is very useful. Find roots, understand shape of graph and turning points.From sketch we can see the exact areas we are being asked to find and note that some of the area is below the x axis and as such 'negative area'.We will use integration to find the area specified but separating the limits to find the area above and below the area separately.Can see areas are equal in magnitude and so would cancel each other out if integrated as one, introduces idea the two sides of the graph are symmetrical and in future questions we can use this idea to speed up workings.